Selected Solutions of Einstein’s Field Equations: Their Role in General Relativity and Astrophysics

  • Jiří Bičák
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 540)

Abstract

The primary purpose of all physical theory is rooted in reality, and most relativists pretend to be physicists. We may often be members of departments of mathematics and our work oriented towards the mathematical aspects of Einstein’s theory, but even those of us who hold a permanent position on “scri”, are primarily looking there for gravitational waves. Of course, the builder of this theory and its field equations was the physicist. Jürgen Ehlers has always been very much interested in the conceptual and axiomatic foundations of physical theories and their rigorous, mathematically elegant formulation; but he has also developed and emphasized the importance of such areas of relativity as kinetic theory, the mechanics of continuous media, thermodynamics and, more recently, gravitational lensing. Feynman expressed his view on the relation of physics to mathematics as follows [1]:

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Feynman, R. (1992) The Character of Physical Law, Penguin books edition, with Introduction by Paul Davies; the original edition published in 1965Google Scholar
  2. 2.
    Hartle, J. B., Hawking, S. W. (1983) Wave function of the Universe, Phys. Rev. D28, 2960. For more recent developments, see Page, D. N. (1991) Minisuperspaces with conformally and minimally coupled scalar fields, J. Math. Phys. 32, 3427, and references thereinMathSciNetGoogle Scholar
  3. 3.
    Kuchař, K. V. (1994) private communication based on unpublished calculations. See also Peleg, Y. (1995) The spectrum of quantum dust black holes, Phys. Lett. B356, 462Google Scholar
  4. 4.
    Chandrasekhar, S. (1987) Ellipsoidal Figures of Equilibrium, Dover paperback edition, Dover Publ., Mineola, N. Y.Google Scholar
  5. 5.
    Tassoul, J.-L. (1978) Theory of Rotating Stars, Princeton University Press, Princeton, N. J.Google Scholar
  6. 6.
    Binney, J., Tremaine, S. (1987) Galactic Dynamics, Princeton University Press, Princeton. The idea first appeared in the work of Kuzmin, G. G. (1956) Astr. Zh. 33, 27MATHGoogle Scholar
  7. 7.
    Taniguchi, K. (1999) Irrotational and Incompressible Binary Systems in the First post-Newtonian Approximation of General Relativity, Progr. Theor. Phys. 101, 283. For an extensive review, see Taniguchi, K. (1999) Ellipsoidal Figures of Equilibrium in the First post-Newtonian Approximation of General Relativity, Thesis, Department of Physics, Kyoto UniversityADSCrossRefGoogle Scholar
  8. 8.
    Ablowitz, M. J., Clarkson, P. A. (1991) Solitons, Nonlinear Evolution Equations and Inverse Scattering, London Mathematical Society, Lecture Notes in Mathematics 149, Cambridge University Press, CambridgeGoogle Scholar
  9. 9.
    Mason, L. J., Woodhouse, N. M. J. (1996) Integrability, Self-Duality, and Twistor Theory, Clarendon Press, OxfordMATHGoogle Scholar
  10. 10.
    Atiyah, M. (1998) Roger Penrose—A Personal Appreciation, in The Geometric Universe: Science, Geometry, and the work of Roger Penrose, eds. S. A. Hugget, L. J. Mason, K. P. Tod, S. T. Tsou and N. M. J. Woodhouse, Oxford University Press, OxfordGoogle Scholar
  11. 11.
    Bičák, J. (1989) Einstein’s Prague articles on gravitation, in Proceedings of the 5th M. Grossmann Meeting on General Relativity, eds. D. G. Blair and M. J. Buckingham, World Scientific, Singapore. A more detailed technical account is given in Bičák, J. (1979) Einstein’s route to the general theory of relativity (in Czech), Čs. čas. fyz. A29, 222Google Scholar
  12. 12.
    Einstein, A. (1912) Relativity and Gravitation. Reply to a Comment by M. Abraham (in German), Ann. der Physik 38, 1059ADSCrossRefGoogle Scholar
  13. 13.
    Einstein, A., Grossmann, M. (1913) Outline of a Generalized Theory of Relativity and of a Theory of Gravitation (in German), Teubner, Leipzig; reprinted in Zeits. f. Math. und Physik 62, 225Google Scholar
  14. 14.
    Einstein, A., Grossmann, M. (1914) Covariance Properties of the Field Equations of the Theory of Gravitation Based on the Generalized Theory of Relativity (in German), Zeits. f. Math. und Physik 63, 215ADSGoogle Scholar
  15. 15.
    Pais, A. (1982) ‘Subtle is the Lord...’—The Science and the Life of Albert Einstein, Clarendon Press, OxfordGoogle Scholar
  16. 16.
    Einstein, A. (1915) The Field Equations of Gravitation (in German), König. Preuss. Akad. Wiss. (Berlin) Sitzungsberichte, 844Google Scholar
  17. 17.
    Corry, L., Renn, J. and Stachel, J. (1997) Belated Decision in the Hilbert-Einstein Priority Dispute, Science 278, 1270ADSCrossRefMathSciNetGoogle Scholar
  18. 18.
    Misner, C., Thorne, K. S. and Wheeler, J. A. (1973) Gravitation, W. H. Freeman and Co., San FranciscoGoogle Scholar
  19. 19.
    Wald, R. M. (1984) General Relativity, The University of Chicago Press, ChicagoMATHGoogle Scholar
  20. 20.
    Einstein, A. (1917) Cosmological Considerations in the General Theory of Relativity (in German), König. Preuss. Akad. Wiss. (Berlin) Sitzungsberichte, 142Google Scholar
  21. 21.
    Prosser, V., Folta, J. eds. (1991) Ernst Mach and the Development of Physics, Charles University—Karolinum, PragueGoogle Scholar
  22. 22.
    Barbour, J., Pfister, H. eds. (1995) Mach’s Principle: From Newton’s Bucket to Quantum Gravity, Birkhäuser, Boston-Basel-BerlinMATHGoogle Scholar
  23. 23.
    Lynden-Bell, D., Katz, J. and Bičák J. (1995) Mach’s principle from the relativistic constraint equations, Mon. Not. Roy. Astron. Soc. 272, 150; Errata: Mon. Not. Astron. Soc. 277, 1600ADSGoogle Scholar
  24. 24.
    Hořava, P. (1999) M theory as a holographic field theory, Phys. Rev. D59, 046004Google Scholar
  25. 25.
    De Sitter, W. (1917) On Einstein’s Theory of Gravitation, and its Astronomical Consequences, Part 3, Mon. Not. Roy. Astron. Soc. 78, 3; see also references thereinADSGoogle Scholar
  26. 26.
    Hawking, S. W., Ellis, G. F. R. (1973) The large scale structure of space-time, Cambridge University Press, CambridgeMATHGoogle Scholar
  27. 27.
    Penrose, R. (1968) Structure of Space-Time, in Batelle Rencontres (1967 Lectures in Mathematics and Physics), eds. C. M. DeWitt and J. A. Wheeler, W. A. Benjamin, New YorkGoogle Scholar
  28. 28.
    Peebles, P. J. E. (1993) Principles of Physical Cosmology, Princeton University Press, PrincetonGoogle Scholar
  29. 29.
    Bertotti, B., Balbinot, R., Bergia, S. and Messina, A. eds. (1990) Modern Cosmology in Retrospect, Cambridge University Press, Cambridge. See especially the contributions by J. Barbour, J. D. North, G. F. R. Ellis, and W. C. Seitter and H. W. DuerbeckGoogle Scholar
  30. 30.
    d’Inverno, R. (1992) Introducing Einstein’s Relativity, Clarendon Press, OxfordMATHGoogle Scholar
  31. 31.
    Geroch, R., Horowitz, G. T. (1979) Global structure of spacetimes, in General Relativity, An Einstein Centenary Survey, eds. S. W. Hawking and W. Israel, Cambridge University Press, CambridgeGoogle Scholar
  32. 32.
    Joshi, P. S. (1993) Global Aspects in Gravitation and Cosmology, Oxford University Press, OxfordMATHGoogle Scholar
  33. 33.
    Schmidt, H. J. (1993) On the de Sitter space-time—the geometric foundation of inflationary cosmology, Fortschr. d. Physik 41, 179ADSGoogle Scholar
  34. 34.
    Eriksen, E., Grøn, O. (1995) The de Sitter universe models, Int. J. Mod. Phys. 4, 115ADSGoogle Scholar
  35. 35.
    Bousso, R. (1998) Proliferation of de Sitter space, Phys. Rev. D58, 083511; see also Bousso, R. (1999) Quantum global structure of de Sitter space, Phys. Rev. D60, 063503Google Scholar
  36. 36.
    Maldacena, J. (1998) The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2, 231MATHADSMathSciNetGoogle Scholar
  37. 37.
    Balasubramanian, V., Kraus, P. and Lawrence, B. (1999) Bulk versus boundary dynamics in anti-de Sitter spacetime, Phys. Rev. D59, 046003Google Scholar
  38. 38.
    Veneziano, G. (1991) Scale factor duality for classical and quantum string, Phys. Lett. B265, 287; Gasperini, M., Veneziano, G. (1993) Pre-big bang in string cosmology, Astropart. Phys. 1, 317. For the most recent review, in which also some answers to the critism of the pre-big-bang scenario and possible observational tests can be found, see Veneziano, G. (1999) Inflating, warming up, and probing the pre-bangian universe, hep th/9902097ADSMathSciNetGoogle Scholar
  39. 39.
    Christodoulou, D., Klainerman, S. (1994) The Global Nonlinear Stability of the Minkowski Spacetime, Princeton University Press, PrincetonGoogle Scholar
  40. 40.
    Bičák, J. (1997) Radiative spacetimes: Exact approaches, in Relativistic Gravitation and Gravitational Radiation (Proceedings of the Les Houches School of Physics), eds. J.-A. Marck and J.-P. Lasota, Cambridge University Press, CambridgeGoogle Scholar
  41. 41.
    Friedrich, H. (1986) On the existence of n-geodesically complete or future complete solutions of Einstein’s field equations with smooth asymptotic structure, Commun. Math. Phys. 107, 587MATHADSCrossRefMathSciNetGoogle Scholar
  42. 42.
    Friedrich, H. (1995) Einstein equations and conformal structure: existence of anti-de Sitter-type space-times, J. Geom. Phys. 17, 125MATHCrossRefADSMathSciNetGoogle Scholar
  43. 43.
    Friedrich, H. (1998) Einstein’s Equation and Geometric Asymptotics, in Gravitation and Relativity: At the turn of the Millenium (Proceedings of the GR-15 conference), eds. N. Dadhich and J. Narlikar, Inter-University Centre for Astronomy and Astrophysics Press, PuneGoogle Scholar
  44. 44.
    Møller, C. (1972) The theory of Relativity, Second Edition, Clarendon Press, OxfordGoogle Scholar
  45. 45.
    Synge, J. L. (1960) Relativity: The General Theory, North-Holland, AmsterdamMATHGoogle Scholar
  46. 46.
    Ehlers, J., Pirani, F. A. E. and Schild, A. (1972) The geometry of free-fall and light propagation, in General Relativity, Papers in Honor of J. L. Synge, ed. L. O. O’Raifeartaigh, Oxford University Press, LondonGoogle Scholar
  47. 47.
    Majer, U., Schmidt, H.-J. eds. (1994) Semantical Aspects of Spacetime Theories, BI-Wissenschaftsverlag, Mannheim, Leipzig, WienGoogle Scholar
  48. 48.
    Misner, C. (1969) Gravitational Collapse, in Brandeis Summer Institute 1968, Astrophysics and General Relativity, eds. M. S. Chrétien, S. Deser and J. Goldstein, Gordon and Breach, New YorkGoogle Scholar
  49. 49.
    Hájček, P. (1999) Choice of gauge in quantum gravity, in Proc. of the 19th Texas symposium on relativistic astrophysics, Paris 1998, to be published; gr-qc/9903089Google Scholar
  50. 50.
    Ehlers, J. (1981) Christoffel’s Work on the Equivalence Problem for Riemannian Spaces and Its Importance for Modern Field Theories of Physics, in E. B. Christoffel: The Influence of His Work on Mathematics and the Physical Sciences, eds. P. L. Butzer, F. Fehér, Birkhäuser Verlag, BaselGoogle Scholar
  51. 51.
    Karlhede, A. (1980) A review of the geometrical equivalence of metrics in general relativity, Gen. Rel. Grav. 12, 693MATHCrossRefADSMathSciNetGoogle Scholar
  52. 52.
    Paiva, F. M., Rebouças, M. J. and MacCallum, M. A. H. (1993) On limits of spacetimes—a coordinate-free approach, Class. Quantum Grav. 10, 1165MATHADSCrossRefGoogle Scholar
  53. 53.
    Ehlers, J., Kundt, K. (1962) Exact Solutions of the Gravitational Field Equations, in Gravitation: an introduction to current research, ed. L. Witten, J. Wiley&Sons, New YorkGoogle Scholar
  54. 54.
    Ehlers, J. (1957) Konstruktionen und Charakterisierungen von Lösungen der Einsteinschen Gravitationsfeldgleichungen, Dissertation, HamburgGoogle Scholar
  55. 55.
    Ehlers, J. (1962) Transformations of static exterior solutions of Einstein’s gravitational field equations into different solutions by means of conformal mappings, in Les Théories Relativistes de la Gravitation, eds. M. A. Lichnerowicz, M. A. Tonnelat, CNRS, ParisGoogle Scholar
  56. 56.
    Ehlers, J. (1965) Exact solutions, in International Conference on Relativistic Theories of Gravitation, Vol. II, London (mimeographed)Google Scholar
  57. 57.
    Jordan, P., Ehlers, J. and Kundt, W. (1960) Strenge Lösungen der Feldgleichungen der Allgemeinen Relativitätstheorie, Akad. Wiss. Lit. Mainz, Abh. Math. Naturwiss. Kl., Nr. 2Google Scholar
  58. 58.
    Jordan, P., Ehlers, J. and Sachs, R. K. (1961) Beiträge zur Theorie der reinen Gravitationsstrahlung, Akad. Wiss. Lit. Mainz, Abh. Math. Naturwiss. Kl., Nr. 1Google Scholar
  59. 59.
    Chandrasekhar, S. (1986) The Aesthetic Base of the General Theory of Relativity. The Karl Schwarzschild lecture, reprinted in Chandrasekhar, S. (1989) Truth and Beauty, Aesthetics and Motivations in Science, The University of Chicago Press, ChicagoGoogle Scholar
  60. 60.
    Chandrasekhar, S. (1975) Shakespeare, Newton, and Beethoven or Patterns of Creativity. The Nora and Edward Ryerson Lecture, reprinted in Chandrasekhar, S. (1989) Truth and Beauty, Aesthetics and Motivations in Science, The University of Chicago Press, ChicagoGoogle Scholar
  61. 61.
    Kramer, D., Stephani, H., Herlt, E. and MacCallum, M. A. H. (1980) Exact solutions of Einstein’s field equations, Cambridge University Press, CambridgeMATHGoogle Scholar
  62. 62.
    Penrose, R. (1999) private communication; see the paper which will appear in special issue of Class. Quantum Gravity celebrating the anniversary of the Institute of PhysicsGoogle Scholar
  63. 63.
    Einstein, A. (1950) Physics and Reality, in Out of My Later Years, Philosophical Library, New York. Originally published in the Journal of the Franklin Institute 221, No. 3; March, 1936Google Scholar
  64. 64.
    Bonnor, W. B. (1992) Physical Interpretation of Vacuum Solutions of Einstein’s Equations. Part I. Time-independent solutions, Gen. Rel. Grav. 24, 551CrossRefADSMathSciNetGoogle Scholar
  65. 65.
    Bonnor, W. B., Griffiths, J. B. and MacCallum, M. A. H. (1994) Physical Interpretation of Vacuum Solutions of Einstein’s Equations. Part II. Timedependent solutions, Gen. Rel. Grav. 26, 687MATHCrossRefADSMathSciNetGoogle Scholar
  66. 66.
    Bondi, H., van der Burg, M. G. J. and Metzner, A. W. K. (1962) Gravitational Waves in General Relativity. VII. Waves from Axi-symmetric Isolated Systems, Proc. Roy. Soc. Lond. A 269, 21MATHGoogle Scholar
  67. 67.
    Ehlers, J. (1973) Survey of General Relativity Theory, in Relativity, Astrophysics and Cosmology, ed. W. Israel, D. Reidel, DordrechtGoogle Scholar
  68. 68.
    Künzle, H. P. (1967) Construction of singularity-free spherically symmetric space-time manifolds, Proc. Roy. Soc. Lond. A297, 244Google Scholar
  69. 69.
    Schmidt, B. G. (1967) Isometry groups with surface-orthogonal trajectories, Zeits. f. Naturfor. 22a, 1351ADSGoogle Scholar
  70. 70.
    Israel, W. (1987) Dark stars: the evolution of an idea, in 300 years of gravitation, eds. S. W. Hawking and W. Israel, Cambridge University Press, CambridgeGoogle Scholar
  71. 71.
    Ciufolini, I., Wheeler, J. A. (1995) Gravitation and Inertia, Princeton University Press, PrincetonMATHGoogle Scholar
  72. 72.
    Will, C. M. (1996) The Confrontation between General Relativity and Experiment: A 1995 Update, in General Relativity (Proceedings of the 46th Scottish Universities Summer School in Physics), eds. G. S. Hall and J. R. Pulham, Institute of Physics Publ., BristolGoogle Scholar
  73. 73.
    Schneider, P., Ehlers, J. and Falco, E. E. (1992) Gravitational Lenses, Springer-Verlag, BerlinCrossRefGoogle Scholar
  74. 74.
    Hawking, S. W. (1973) The Event Horizon, in Black Holes (Les Houches 1972), eds. C. DeWitt and B. S. DeWitt, Gordon and Breach, New York-London-ParisGoogle Scholar
  75. 75.
    Thorne, K. S., Price, R. H. and MacDonald, D. A. (1986) Black Holes: The Membrane Paradigm, Yale University Press, New HavenGoogle Scholar
  76. 76.
    Frolov, V., Novikov, I. (1998) Physics of Black Holes, Kluwer, DordrechtGoogle Scholar
  77. 77.
    Clarke, C. J. S. (1993) The Analysis of Space-Time Singularieties, Cambridge University Press, CambridgeGoogle Scholar
  78. 78.
    Boyer, R. H. (1969) Geodesic Killing orbits and bifurcate Killing horizons, Proc. Roy. Soc. (London) A311, 245MathSciNetGoogle Scholar
  79. 79.
    Carter, B. (1972) Black Hole Equilibrium States, in Black Holes (Les Houches 1972), eds. C. De Witt and B. S. De Witt, Gordon and Breach, New York-London-ParisGoogle Scholar
  80. 80.
    Chruściel, P. T. (1996) Uniqueness of stationary, electro-vacuum black holes revisited, Helv. Phys. Acta 69, 529MATHADSMathSciNetGoogle Scholar
  81. 81.
    Heusler, M. (1996) Black Hole Uniqueness Theorems, Cambridge University Press, CambridgeMATHGoogle Scholar
  82. 82.
    Wald, R. M. (1994) Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, The University of Chicago Press, ChicagoMATHGoogle Scholar
  83. 83.
    Rácz, I., Wald R. M. (1996) Global extensions of spacetimes describing asymptotic final states of black holes, Class. Quantum Grav. 13, 539MATHADSCrossRefGoogle Scholar
  84. 84.
    Penrose, R. (1980) On Schwarzschild Causality—A Problem for “Lorentz Covariant” General Relativity, in Essays in General Relativity, eds. F. J. Tipler, Academic Press, New YorkGoogle Scholar
  85. 85.
    Weinberg, S., Gravitation and Cosmology (1972) J. Wiley, New York (see in particular Ch. 6, part 9)Google Scholar
  86. 86.
    Zel’dovich, Ya. B., Grishchuk, L. P. (1988) The general theory of relativity is correct!, Sov. Phys. Usp. 31, 666. This very pedagogical paper contains a number of references on the field-theoretical approach to gravityCrossRefMathSciNetADSGoogle Scholar
  87. 87.
    Ehlers, J. (1998) General Relativity as Tool for Astrophysics, in Relativistic Astrophysics, eds. H. Riffert et al., Vieweg, Braunschweig/WiesbadenGoogle Scholar
  88. 88.
    Rees, M. (1998) Astrophysical Evidence for Black Holes, in Black Holes and Relativistic Stars, ed. R. M. Wald, The University of Chicago Press, ChicagoGoogle Scholar
  89. 89.
    Menou, K., Quataert, E. and Narayan, R. (1998) Astrophysical Evidence for Black Hole Event Horizons, in Gravitation and Relativity: At the turn of the Millennium (Proceedings of the GR-15 Conference), eds. N. Dadhich and J. Narlikar, Inter-University Centre for Astronomy and Astrophysics Press, Pune; also astro-ph/9712015Google Scholar
  90. 90.
    Carr, B. J. (1996) Black Holes in Cosmology and Astrophysics, in General Relativity (Proceedings of the 46th Scottish Universities Summer School in Physics), eds. G. S. Hall and J. R. Pulham, Institute of Physics Publishing, LondonGoogle Scholar
  91. 91.
    Chandrasekhar, S. (1984) The Mathematical Theory of Black Holes, Clarendon Press, OxfordGoogle Scholar
  92. 92.
    Abramowicz, M. A. (1993) Inertial forces in general relativity, in The Renaissance of General Relativity and Cosmology, eds. G. Ellis, A. Lanza and J. Miller, Cambridge University Press, CambridgeGoogle Scholar
  93. 93.
    Semerák, O. (1998) Rotospheres in Stationary Axisymmetric Spacetimes, Ann. Phys. (N.Y.) 263, 133; see also 69 references quoted thereinMATHADSCrossRefGoogle Scholar
  94. 94.
    Feynman, R. P., Morinigo, F. B., Wagner W. G. (1995) Feynman lectures on gravitation, Addison-Wesley Publ. Co., Reading, Mass.Google Scholar
  95. 95.
    Shapiro, S. L., Teukolsky, S. A. (1983) Black Holes, White Dwarfs, and Neutron Stars, J. Wiley, New YorkGoogle Scholar
  96. 96.
    Frank, J., King, A. and Raine, D. (1992) Accretion Power in Astrophysics, 2nd edition, Cambridge University Press, CambridgeGoogle Scholar
  97. 97.
    Thorne, K. S. (1998) Probing Black Holes and Relativistic Stars with Gravitational Waves, in Black Holes and Relativistic Stars, ed. R. M. Wald, The University of Chicago Press, Chicago. See also lectures by E. Seidel, J. Pullin, and E. Flanagan, in Gravitation and Relativity: At the turn of the Millennium (Proceedings of the GR-15 Conference), eds. N. Dadhich and J. Narlikar, Inter-University Centre for Astronomy and Astrophysics Press, PuneGoogle Scholar
  98. 98.
    Pullin, J. (1998) Colliding Black Holes: Analytic Insights, in Gravitation and Relativity: At the turn of the Millennium (Proceedings of the GR-15 Conference), eds. N. Dadhich and J. Narlikar, Inter-University Centre for Astronomy and Astrophysics Press, PuneGoogle Scholar
  99. 99.
    Graves, J. C., Brill, D. R. (1960) Oscillatory character of Reissner-Nordström metric for an ideal charged wormhole, Phys. Rev. 120, 1507MATHADSCrossRefMathSciNetGoogle Scholar
  100. 100.
    Boulware, D. G. (1973) Naked Singularities, Thin Shells, and the Reissner-Nordström Metric, Phys. Rev. D8, 2363ADSMathSciNetGoogle Scholar
  101. 101.
    Zel’dovich, Ya. B., Novikov, I. D. (1971) Relativistic Astrophysics, Volume 1: Stars and Relativity, The University of Chicago Press, ChicagoGoogle Scholar
  102. 102.
    Penrose, R. (1979) Singularities and time-asymmetry, in General Relativity, An Einstein Centenary Survey, eds. S. W. Hawking and W. Israel, Cambridge University Press, CambridgeGoogle Scholar
  103. 103.
    Burko, L., Ori, A. (1997) Introduction to the internal structure of black holes, in Internal Structure of Black Holes and Spacetime Singularities, eds. L. Burko and A. Ori, Inst. Phys. Publ., Bristol, and The Israel Physical Society, JerusalemGoogle Scholar
  104. 104.
    Bičák, J., Dvořák, L. (1980) Stationary electromagnetic fields around black holes III. General solutions and the fields of current loops near the Reissner-Nordström black hole, Phys. Rev. D22, 2933ADSGoogle Scholar
  105. 105.
    Moncrief, V. (1975) Gauge-invariant perturbations of Reissner-Nordström black holes, Phys. Rev. D12, 1526; see also references thereinADSGoogle Scholar
  106. 106.
    Bičák, J. (1979) On the theories of the interacting perturbations of the Reissner-Nordström black hole, Czechosl. J. Phys. B29, 945ADSGoogle Scholar
  107. 107.
    Bičák, J. (1972) Gravitational collapse with charge and small asymmetries, I: Scalar perturbations, Gen. Rel. Grav. 3, 331ADSCrossRefGoogle Scholar
  108. 108.
    Price, R. H. (1972) Nonspherical perturbations of relativistic gravitational collapse, I: Scalar and gravitational perturbations, Phys. Rev. D5, 2419ADSMathSciNetGoogle Scholar
  109. 109.
    Price, R. H. (1972) Nonspherical perturbations of relativistic gravitational collapse, II: Integer-spin, zero-rest-mass fields, Phys. Rev. D5, 2439Google Scholar
  110. 110.
    Bičák, J. (1980) Gravitational collapse with charge and small asymmetries, II: Interacting electromagnetic and gravitational perturbations, Gen. Rel. Grav. 12, 195ADSCrossRefGoogle Scholar
  111. 111.
    Poisson, E., Israel, W. (1990) Internal structure of black holes, Phys. Rev. D41, 1796ADSMathSciNetGoogle Scholar
  112. 112.
    Bonnor, W. B., Vaidya, P. C. (1970) Spherically Symmetric Radiation of Charge in Einstein-Maxwell Theory, Gen. Rel. Grav. 1, 127CrossRefADSMathSciNetGoogle Scholar
  113. 113.
    Chambers, C. M. (1997) The Cauchy horizon in black hole-de Sitter spacetimes, in Internal Structure of Black Holes and Spacetime Singularities, eds. L. Burko and A. Ori, Inst. Phys. Publ. Bristol, and The Israel Physical Society, JerusalemGoogle Scholar
  114. 114.
    Penrose, R. (1998) The Question of Cosmic Censorship, in Black Holes and Relativistic Stars, ed. R. M. Wald, The University of Chicago Press, ChicagoGoogle Scholar
  115. 115.
    Brady, P. R., Moss, I. G. and Myers, R. C. (1998) Cosmic Censorship: As Strong As Ever, Phys. Rev. Lett. 80, 3432MATHADSCrossRefMathSciNetGoogle Scholar
  116. 116.
    Hubený, V. E. (1999) Overcharging a Black Hole and Cosmic Censorship, Phys. Rev. D59, 064013Google Scholar
  117. 117.
    Bičák, J. (1977) Stationary interacting fields around an extreme Reissner-Nordström black hole, Phys. Lett. 64A, 279. See also the review Bičák, J. (1982), Perturbations of the Reissner-Nordström black hole, in the Proceedings of the Second Marcel Grossmann Meeting on General Relativity, ed. R. Ruffini, North-Holland, Amsterdam, and references thereinADSGoogle Scholar
  118. 118.
    Hájíček, P. (1981) Quantum wormholes (I.) Choice of the classical solution, Nucl. Phys. B185, 254ADSCrossRefGoogle Scholar
  119. 119.
    Aichelburg, P. C., Güven, R. (1983) Remarks on the linearized superhair, Phys. Rev. D27, 456; and references thereinADSGoogle Scholar
  120. 120.
    Schwarz, J. H., Seiberg, N. (1999) String theory, supersymmetry, unification, and all that, Rev. Mod. Phys. 71, S112CrossRefGoogle Scholar
  121. 121.
    Carlip, S. (1995) The (2+1)-dimensional black hole, Class. Quantum Grav. 12, 2853MATHADSCrossRefMathSciNetGoogle Scholar
  122. 122.
    Myers, R. C., Perry, M. J. (1986) Black holes in higher dimensional spacetimes, Ann. Phys. (N.Y.) 172, 304MATHADSCrossRefMathSciNetGoogle Scholar
  123. 123.
    Gibbons, G. W., Horowitz, G. T. and Townsend, P. K. (1995) Higherdimensional resolution of dilatonic black-hole singularities, Class. Quantum Grav. 12, 297MATHADSCrossRefMathSciNetGoogle Scholar
  124. 124.
    Horowitz, G. T., Teukolsky, S. A. (1999) Black holes, Rev. Mod. Phys. 71, S180ADSCrossRefGoogle Scholar
  125. 125.
    Wald, R. M. (1998) Black Holes and Thermodynamics, in Black Holes and Relativistic Stars, ed. R. M. Wald, The University of Chicago Press, ChicagoGoogle Scholar
  126. 126.
    Horowitz, G. T. (1998) Quantum States of Black Holes, in Black Holes and Relativistic Stars, ed. R. M. Wald, the University of Chicago Press, ChicagoGoogle Scholar
  127. 127.
    Skenderis, K. (1999) Black holes and branes in string theory, hep-th/9901050Google Scholar
  128. 128.
    Ashtekhar, A., Baez, J., Corichi, A. and Krasnov, K. (1998) Quantum Geometry and Black Hole Entropy, Phys. Rev. Lett. 80, 904ADSCrossRefMathSciNetGoogle Scholar
  129. 129.
    Youm, D. (1999) Black holes and solitons in string theory, Physics Reports 316, Nos. 1–3, 1ADSCrossRefMathSciNetGoogle Scholar
  130. 130.
    Chamblin, A., Emparan, R. and Gibbons, G. W. (1998) Superconducting pbranes and extremal black holes, Phys. Rev. D58, 084009Google Scholar
  131. 131.
    Ernst, F. J. (1976) Removal of the nodal singularity of the C-metric, J. Math. Phys. 17, 54; see also Ernst, F. J., Wild, W. J. (1976) Kerr black holes in a magnetic universe, J. Math. Phys. 17, 182ADSCrossRefMathSciNetGoogle Scholar
  132. 132.
    Karas, V., Vokrouhlický, D. (1991) On interpretation of the magnetized Kerr-Newman black hole, J. Math. Phys. 32, 714MATHADSCrossRefMathSciNetGoogle Scholar
  133. 133.
    Kerr, R. P. (1963) Gravitational field of a spinning mass as an example of algebraically special metrics, Phys. Rev. Lett. 11, 237MATHADSCrossRefMathSciNetGoogle Scholar
  134. 134.
    Stewart, J., Walker, M. (1973) Black holes: the outside story, in Springer tracts in modern physics, Vol. 69, Springer-Verlag, BerlinGoogle Scholar
  135. 135.
    Thorne, K. S. (1980) Multipole expansions of gravitational radiation, Rev. Mod. Phys. 52, 299ADSCrossRefMathSciNetGoogle Scholar
  136. 136.
    Hansen, R. O. (1974) Multipole moments of stationary space-times, J. Math. Phys. 15, 46MATHCrossRefADSGoogle Scholar
  137. 137.
    Beig, R., Simon, W. (1981) On the multipole expansion for stationary spacetimes, Proc. Roy. Soc. Lond. A376, 333MathSciNetGoogle Scholar
  138. 138.
    de Felice, F., Clarke, C. J. S. (1990) Relativity on curved manifolds, Cambridge University Press, CambridgeMATHGoogle Scholar
  139. 139.
    Landau, L. D., Lifshitz, E. M. (1962) The Classical Theory of Fields, Pergamon Press, OxfordMATHGoogle Scholar
  140. 140.
    O’Neill, B. (1994) The Geometry of Kerr Black Holes, A. K. Peters, WellesleyGoogle Scholar
  141. 141.
    Katz, J., Lynden-Bell, D. and Bičák, J. (1998) Instantaneous inertial frames but retarded electromagnetism in rotating relativistic collapse, Class. Quantum Grav. 15, 3177MATHADSCrossRefGoogle Scholar
  142. 142.
    Semerák, O. (1996) Photon escape cones in the Kerr field, Helv. Phys. Acta 69, 69MATHADSMathSciNetGoogle Scholar
  143. 143.
    Bičák, J., Stuchlík, Z. (1976) The fall of the shell of dust onto a rotating black hole, Mon. Not. Roy. Astron. Soc. 175, 381ADSGoogle Scholar
  144. 144.
    Bičák, J., Semerák, O. and Hadrava, P. (1993) Collimation effects of the Kerr field, Mon. Not. Roy. Astron. Soc. 263, 545ADSGoogle Scholar
  145. 145.
    Newman, E. T., Couch, E., Chinnapared, K., Exton, A., Prakash, A. and Torrence, R. (1965) Metric of a rotating charged mass, J. Math. Phys. 6, 918CrossRefADSMathSciNetGoogle Scholar
  146. 146.
    Garfinkle, D., Traschen, J. (1990) Gyromagnetic ratio of a black hole, Phys. Rev. D42, 419ADSGoogle Scholar
  147. 147.
    Bardeen, J. M. (1973) Timelike and Null Geodesics in the Kerr Metric, in Black Holes, eds. C. DeWitt and B. S. DeWitt, Gordon and Breach, New YorkGoogle Scholar
  148. 148.
    Rindler, W. (1997) The case against space dragging, Phys. Lett. A233, 25ADSMathSciNetGoogle Scholar
  149. 149.
    Jantzen, R. T., Carini, P. and Bini, D. (1992) The Many Faces of Gravitoelectromagnetism, Ann. Phys. (N.Y.) 215, 1; see also the review (1999) The Inertial Forces / Test Particle Motion Game, in the Proceedings of the 8th M. Grossmann Meeting on General Relativity, ed. T. Piran, World Scientific, SingaporeADSCrossRefMathSciNetGoogle Scholar
  150. 150.
    Karas, V., Vokrouhlický, D. (1994) Relativistic precession of the orbit of a star near a supermassive rotating black hole, Astrophys. J. 422, 208ADSCrossRefGoogle Scholar
  151. 151.
    Blandford, R. D., Znajek, R. L. (1977) Electromagnetic extraction of energy from Kerr black holes, Mon. Not. Roy. Astron. Soc. 179,433. See also Blandford, R. (1987) Astrophysical black holes, in 300 years of gravitation, eds. S. W. Hawking and W. Israel, Cambridge University Press, CambridgeADSGoogle Scholar
  152. 152.
    Bičák, J., Janiš, V. (1985) Magnetic fluxes across black holes, Mon. Not. Roy. Astron. Soc. 212, 899ADSGoogle Scholar
  153. 153.
    Punsly, B., Coroniti, F. V. (1990) Relativistic winds from pulsar and black hole magnetospheres, Astrophys. J. 350, 518. See also Punsly, B. (1998) Highenergy gamma-ray emission from galactic Kerr-Newman black holes. The central engine, Astrophys. J. 498, 640, and references thereinADSCrossRefGoogle Scholar
  154. 154.
    Abramowicz, M. (1998) private communicationGoogle Scholar
  155. 155.
    Mirabel, I. F., Rodríguez, L. F. (1998) Microquasars in our Galaxy, Nature 392, 673ADSCrossRefGoogle Scholar
  156. 156.
    Futterman, J. A. H., Handler, F. A. and Matzner, R. A. (1988) Scattering from black holes, Cambridge University Press, CambridgeMATHGoogle Scholar
  157. 157.
    Bičák, J., Dvořák, L. (1976) Stationary electromagnetic fields around black holes II. General solutions and the fields of some special sources near a Kerr black hole, Gen. Rel. Grav. 7, 959ADSCrossRefGoogle Scholar
  158. 158.
    Sasaki, M., Nakamura, T. (1990) Gravitational Radiation from an Extreme Kerr Black Hole, Gen. Rel. Grav. 22, 1551; and references thereinCrossRefMathSciNetGoogle Scholar
  159. 159.
    Krivan, W., Price, R. H. (1999) Formation of a rotating Black Hole from a Close-Limit Head-On Collision, Phys. Rev. Lett. 82, 1358MATHADSCrossRefMathSciNetGoogle Scholar
  160. 160.
    Campanelli, M., Lousto, C. O. (1999) Second order gauge invariant gravitational perturbations of a Kerr black hole, Phys. Rev. D59, 124022ADSMathSciNetGoogle Scholar
  161. 161.
    Fabian, A. C. (1999) Emission lines: signatures of relativistic rotation, in Theory of Accretion Disks, eds. M. Abramowicz, G. Björnson, J. Pringle, Cambridge University Press, CambridgeGoogle Scholar
  162. 162.
    Ipser, J. R. (1998) Low-Frequency Oscillations of Relativistic Accretion Disks, in Relativistic Astrophysics, eds. [edH. Riffert et al.}, Vieweg, Braunschweig, WiesbadenGoogle Scholar
  163. 163.
    Bičák, J., Podolský, J. (1997) The global structure of Robinson-Trautman radiative space-times with cosmological constant, Phys. Rev. D55, 1985ADSGoogle Scholar
  164. 164.
    Hartle, J. B., Hawking, S. W. (1972) Solutions of the Einstein-Maxwell equations with many black holes, Commun. Math. Phys. 26, 87ADSCrossRefMathSciNetGoogle Scholar
  165. 165.
    Heusler, M. (1997) On the Uniqueness of the Papapetrou-Majumdar metric, Class. Quantum Grav. 14, L129ADSCrossRefMathSciNetGoogle Scholar
  166. 166.
    Chruściel, P. T. (1999) Towards the classification of static electro-vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior, Class. Quantum Grav. 16, 689. See also Chruściel’s very general result for the vacuum case in the preceding paper: The classification of static vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior, Class. Quantum Grav. 16, 661ADSCrossRefMATHGoogle Scholar
  167. 167.
    Kramer, D., Neugebauer, G. (1984) Bäcklund Transformations in General Relativity, in Solutions of Einstein’s Equations: Techniques and Results, eds. C. Hoenselaers and W. Dietz, Lecture Notes in Physics 205, Springer-Verlag, BerlinCrossRefGoogle Scholar
  168. 168.
    Bičák, J., Hoenselaers, C. (1985) Two equal Kerr-Newman sources in stationary equilibrium, Phys. Rev. D31, 2476ADSGoogle Scholar
  169. 169.
    Weinstein, G. (1996) N-black hole stationary and axially symmetric solutions of the Einstein/Maxwell equations, Comm. Part. Di.. Eqs. 21, 1389MATHCrossRefGoogle Scholar
  170. 170.
    Dietz, W., Hoenselaers, C. (1982) Stationary System of Two Masses Kept Apart by Their Gravitational Spin-Spin Interaction, Phys. Rev. Lett. 48, 778; see also Dietz, W. (1984) HKX-Transformations: Some Results, in Solutions of Einstein’s Equations: Techniques and Results, eds. C. Hoenselaers and W. Dietz, Lecture Notes in Physics 205, Springer-Verlag, BerlinADSCrossRefMathSciNetGoogle Scholar
  171. 171.
    Kastor, D., Traschen, J. (1993) Cosmological multi-black-hole solutions, Phys. Rev. D47, 5370ADSMathSciNetGoogle Scholar
  172. 172.
    Brill, D. R., Horowitz, G. T., Kastor, D. and Traschen, J. (1994) Testing cosmic censorship with black hole collisions, Phys. Rev. D49, 840ADSMathSciNetGoogle Scholar
  173. 173.
    Welch, D. L. (1995) Smoothness of the horizons of multi-black-hole solutions, Phys. Rev. D52, 985ADSMathSciNetGoogle Scholar
  174. 174.
    Brill, D. R., Hayward, S. A. (1994) Global structure of a black hole cosmos and its extremes, Class. Quantum Grav. 11, 359MATHADSCrossRefMathSciNetGoogle Scholar
  175. 175.
    Ida, D., Nakao, K., Siino, M. and Hayward, S. A. (1998) Hoop conjecture for colliding black holes, Phys. Rev. D58, 121501ADSMathSciNetGoogle Scholar
  176. 176.
    Scott, S. M., Szekeres, P. (1986) The Curzon singularity I: spatial section, Gen. Rel. Grav. 18, 557; The Curzon singularity II: global picture, Gen. Rel. Grav. 18, 571MATHADSCrossRefMathSciNetGoogle Scholar
  177. 177.
    Bičák, J., Lynden-Bell, D. and Katz, J. (1993) Relativistic disks as sources of static vacuum spacetimes, Phys. Rev. D47, 4334ADSGoogle Scholar
  178. 178.
    Bičák, J., Lynden-Bell, D. and Pichon, C. (1993) Relativistic discs and flat galaxy models, Mon. Not. Roy. Astron. Soc. 265, 26Google Scholar
  179. 179.
    Evans, N. W., de Zeeuw, P. T. (1992) Potential-density pairs for flat galaxies, Mon. Not. Roy. Astron. Soc. 257, 152ADSGoogle Scholar
  180. 180.
    Chruściel, P., MacCallum, M. A. H. and Singleton, P. B. (1995) Gravitational waves in general relativity XIV. Bondi expansions and the ‘polyhomogeneity’ of J, Phil. Trans. Roy. Soc. Lond. A350, 113ADSCrossRefGoogle Scholar
  181. 181.
    Semerák, O., Zellerin, T. and Žáček, M. (1999) The structure of superposed Weyl fields, Mon. Not. Roy. Astron. Soc., 308, 691 and 705ADSCrossRefGoogle Scholar
  182. 182.
    Lemos, J. P. S., Letelier, P. S. (1994) Exact general relativistic thin disks around black holes, Phys. Rev. D49, 5135ADSGoogle Scholar
  183. 183.
    González, G. A., Letelier, P. S. (1999) Relativistic Static Thin Disks with Radial Stress Support, Class. Quantum Grav. 16, 479MATHADSCrossRefGoogle Scholar
  184. 184.
    Letelier, P. S. (1999) Exact General Relativistic Disks with Magnetic Fields, gr-qc/9907050Google Scholar
  185. 185.
    Krasiński, A. (1978) Sources of the Kerr metric, Ann. Phys. (N.Y.) 112, 22ADSCrossRefMATHGoogle Scholar
  186. 186.
    McManus, D. (1991) A toroidal source for the Kerr black hole geometry, Class. Quantum Grav. 8, 863ADSCrossRefMathSciNetGoogle Scholar
  187. 187.
    Bardeen, J. M., Wagoner, R. V. (1971) Relativistic disks. I. Uniform rotation, Astrophys. J. 167, 359ADSCrossRefMathSciNetGoogle Scholar
  188. 188.
    Bičák, J., Ledvinka, T. (1993) Relativistic Disks as Sources of the Kerr Metric, Phys. Rev. Lett. 71, 1669. See also (1993) Sources for stationary axisymmetric gravitational fields, Max-Planck-Institute for Astrophysics, Green report MPA 726, MunichADSCrossRefMATHMathSciNetGoogle Scholar
  189. 189.
    Pichon, C., Lynden-Bell, D. (1996) New sources for Kerr and other metrics: rotating relativistic discs with pressure support, Mon. Not. Roy. Astron. Soc. 280, 1007ADSGoogle Scholar
  190. 190.
    Barrabés, C., Israel, W. (1991) Thin shells in general relativity and cosmology: the lightlike limit, Phys. Rev. D43, 1129ADSGoogle Scholar
  191. 191.
    Ledvinka, T., Bičák, J. and Žofka, M. (1999) Relativistic disks as sources of Kerr-Newman fields, in Proc. 8th M. Grossmann Meeting on General Relativity, ed. T. Piran, World Sci., SingaporeGoogle Scholar
  192. 192.
    Neugebauer, G., Meinel, R. (1995) General Relativistic Gravitational Fields of a Rigidly Rotating Disk of Dust: Solution in Terms of Ultraelliptic Functions, Phys. Rev. Lett. 75, 3046MATHADSCrossRefMathSciNetGoogle Scholar
  193. 193.
    Neugebauer, G., Kleinwächter, A. and Meinel, R. (1996) Relativistically rotating dust, Helv. Phys. Acta 69, 472MATHADSGoogle Scholar
  194. 194.
    Meinel, R. (1998) The rigidly rotating disk of dust and its black hole limit, in Proc. of the Second Mexican School on Gravitation and Mathematical Physics, eds. A. Garcia et al., Science Network Publishing, Konstanz, gr-qc/9703077Google Scholar
  195. 195.
    Breitenlohner, P., Forgács, P. and Maison, D. (1995) Gravitating Monopole Solutions II, Nucl. Phys. 442B, 126ADSGoogle Scholar
  196. 196.
    Misner, Ch. (1967) Taub-NUT Space as a Counterexample to Almost Anything, in Relativity Theory and Astrophysics 1, Lectures in Applied Mathematics, Vol. 8, ed. J. Ehlers, American Math. Society, Providence, R. I.Google Scholar
  197. 197.
    Taub, A. H. (1951) Empty space-times admitting a three parameter group of motions, Ann. Math. 53, 472CrossRefADSMathSciNetGoogle Scholar
  198. 198.
    Newman, E., Tamburino, L. and Unti, T. (1963) Empty-space generalization of the Schwarzschild metric, J. Math. Phys. 4, 915MATHCrossRefADSMathSciNetGoogle Scholar
  199. 199.
    Lynden-Bell, D., Nouri-Zonoz, M. (1998) Classical monopoles: Newton, NUT space, gravomagnetic lensing, and atomic spectra, Rev. Mod. Phys. 70, 427ADSCrossRefMathSciNetGoogle Scholar
  200. 200.
    Geroch, R. (1971) A method for generating solutions of Einsteinr’s equations, J. Math. Phys. 12, 918 and J. Math. Phys. 13, 394MATHCrossRefADSMathSciNetGoogle Scholar
  201. 201.
    Ehlers, J. (1997) Examples of Newtonian limits of relativistic spacetimes, Class. Quantum Grav. 14, A119MATHADSCrossRefMathSciNetGoogle Scholar
  202. 202.
    Wheeler, J. A. (1980) The Beam and Stay of the Taub Universe, in Essays in General Relativity, eds. F. J. Tipler, Academic Press, New YorkGoogle Scholar
  203. 203.
    Hájíček, P. (1971) Extension of the Taub and NUT spaces and extensions of their tangent bundles, Commun. Math. Phys. 17, 109; Bifurcate spacetimes, J. Math. Phys. 12, 157; Causality in non-Hausdor. spacetimes, Commun. Math. Phys. 21, 75CrossRefGoogle Scholar
  204. 204.
    Thorne, K. S. (1993) Misner Space as a Prototype for Almost Any Pathology, in Directions in General Relativity, Vol. 1, eds. B. L. Hu, M. P. Ryan and C. V. Vishveshwara, Cambridge University Press, CambridgeGoogle Scholar
  205. 205.
    Gibbons, G. W., Manton, N. S. (1986) Classical and Quantum Dynamics of BPS monopoles, Nuclear Physics B274, 183ADSMathSciNetGoogle Scholar
  206. 206.
    Kraan T. C., Baal P. (1998) Exact T-duality between calorons and Taub—NUT spaces, INLO-PUB-4/98, hep-th/9802049Google Scholar
  207. 207.
    Bičák, J., Podolský, J. (1999) Gravitational waves in vacuum spacetimes with cosmological constant. I. Classification and geometrical properties of nontwisting type N solutions. II. Deviation of geodesics and interpretation of non-twisting type N solutions, J. Math. Phys. 44, 4495 and 4506ADSCrossRefGoogle Scholar
  208. 208.
    Aichelburg, P. C., Balasin, H. (1996) Symmetries of pp-waves with distributional profile, Class. Quantum Grav. 13, 723MATHADSCrossRefMathSciNetGoogle Scholar
  209. 209.
    Aichelburg, P. C., Balasin, H. (1997) Generalized symmetries of impulsive gravitational waves, Class. Quantum Grav. 14, A31MATHADSCrossRefMathSciNetGoogle Scholar
  210. 210.
    Aichelburg, P. C., Sexl, R. U. (1971) On the gravitational field of a massless particle, Gen. Rel. Grav. 2, 303CrossRefADSGoogle Scholar
  211. 211.
    Penrose, R. (1972) The geometry of impulsive gravitational waves, in General Relativity, Papers in Honour of J. L. Synge, ed. L. O’Raifeartaigh, Clarendon Press, OxfordGoogle Scholar
  212. 212.
    Griffiths, J. B. (1991) Colliding Plane Waves in General Relativity, Clarendon Press, OxfordMATHGoogle Scholar
  213. 213.
    Bondi, H., Pirani, F. A. E. and Robinson, I. (1959) Gravitational waves in general relativity. III. Exact plane waves, Proc. Roy. Soc. Lond. A 251, 519MATHMathSciNetGoogle Scholar
  214. 214.
    Rindler, W. (1977) Essential Relativity (2nd edition), Springer, New York-BerlinMATHGoogle Scholar
  215. 215.
    Penrose, R. (1965) A remarkable property of plane waves in general relativity, Rev. Mod. Phys. 37, 215MATHADSCrossRefMathSciNetGoogle Scholar
  216. 216.
    Lousto, C. O., Sánchez, N. (1989) The ultrarelativistic limit of the Kerr-Newman geometry and particle scattering at the Planck scale, Phys. Lett. B232, 462ADSGoogle Scholar
  217. 217.
    Ferrari, V., Pendenza, P. (1990) Boosting the Kerr Metric, Gen. Rel. Grav. 22, 1105CrossRefADSMathSciNetGoogle Scholar
  218. 218.
    Balasin, H., Nachbagauer, H. (1995) The ultrarelativistic Kerr-geometry and its energy-momentum tensor, Class. Quantum Grav. 12, 707ADSCrossRefMathSciNetGoogle Scholar
  219. 219.
    Podolský, J., Griffiths, J. B. (1998) Boosted static multipole particles as sources of impulsive gravitational waves, Phys. Rev. D58, 124024ADSGoogle Scholar
  220. 220.
    Hotta, M., Tanaka, M. (1993) Shock-wave geometry with non-vanishing cosmological constant, Class. Quantum Grav. 10, 307ADSCrossRefMathSciNetGoogle Scholar
  221. 221.
    Podolský, J., Griffiths, J. B. (1997) Impulsive gravitational waves generated by null particles in de Sitter and anti-de Sitter backgrounds, Phys. Rev. D56, 4756ADSGoogle Scholar
  222. 222.
    D’Eath, P. D. (1996) Black Holes: Gravitational Interactions, Clarendon Press, OxfordMATHGoogle Scholar
  223. 223.
    ’t Hooft, G. (1987) Graviton dominance in ultra-high-energy scattering, Phys. Lett. B198, 61ADSMathSciNetGoogle Scholar
  224. 224.
    Fabbrichesi, M., Pettorino, R., Veneziano, G. and Vilkovisky, G. A. (1994) Planckian energy scattering and surface terms in the gravitational action, Nucl. Phys. B419, 147ADSCrossRefGoogle Scholar
  225. 225.
    Kunzinger, M., Steinbauer, R. (1999) A note on the Penrose junction conditions, Class. Quantum Grav. 16, 1255MATHADSCrossRefMathSciNetGoogle Scholar
  226. 226.
    Kunzinger, M., Steinbauer, R. (1999) A rigorous solution concept for geodesic and geodesic deviation equations in impulsive gravitational waves, J. Math. Phys. 40, 1479MATHADSCrossRefMathSciNetGoogle Scholar
  227. 227.
    Podolský, J., Veselý, K. (1998) Chaotic motion in pp-wave spacetimes, Class. Quantum Grav. 15, 3505MATHADSCrossRefGoogle Scholar
  228. 228.
    Levin, O., Peres, A. (1994) Quantum field theory with null-fronted metrics, Phys. Rev. D50, 7421ADSMathSciNetGoogle Scholar
  229. 229.
    Klimčík, C. (1991) Gravitational waves as string vacua I, II, Czechosl. J. Phys. 41, 697 (see also references therein)ADSCrossRefMATHGoogle Scholar
  230. 230.
    Gibbons, G. W. (1999) Two loop and all loop finite 4-metrics, Class. Quantum Grav. 16, L 71ADSCrossRefMathSciNetGoogle Scholar
  231. 231.
    Bičák, J., Pravda, V. (1998) Curvature invariants in type N spacetimes, Class. Quantum Grav. 15, 1539ADSCrossRefMATHGoogle Scholar
  232. 232.
    Pravda, V. (1999) Curvature invariants in type-III spacetimes, Class. Quantum Grav. 16, 3321MATHADSCrossRefMathSciNetGoogle Scholar
  233. 233.
    Khan, K. A., Penrose, R. (1971) Scattering of two impulsive gravitational plane waves, Nature 229, 185ADSCrossRefGoogle Scholar
  234. 234.
    Szekeres, P. (1970) Colliding gravitational waves, Nature 228, 1183ADSCrossRefGoogle Scholar
  235. 235.
    Szekeres, P. (1972) Colliding plane gravitational waves, J. Math. Phys. 13, 286CrossRefADSMathSciNetGoogle Scholar
  236. 236.
    Yurtsever, U. (1988) Structure of the singularities produced by colliding plane waves, Phys. Rev. D38, 1706ADSMathSciNetGoogle Scholar
  237. 237.
    Hauser, I., Ernst, F. J. (1989) Initial value problem for colliding gravitational waves—I/II, J. Math. Phys. 30, 872 and 2322; (1990) and (1991) Initial value problem for colliding gravitational waves. III/IV, J. Math. Phys. 31, 871 and 32, 198MATHADSCrossRefMathSciNetGoogle Scholar
  238. 238.
    Hauser, I., Ernst, F. J. (1999) Group structure of the solution manifold of the hyperbolic Ernst equation—general study of the subject and detailed elaboration of mathematical proofs, 216 pages, gr-qc/9903104Google Scholar
  239. 239.
    Nutku, Y., Halil, M. (1977) Colliding impulsive gravitational waves, Phys. Rev. Lett. 39, 1379ADSCrossRefGoogle Scholar
  240. 240.
    Matzner, R., Tipler, F. J. (1984) Methaphysics of colliding self-gravitating plane waves, Phys. Rev. D29, 1575ADSMathSciNetGoogle Scholar
  241. 241.
    Chandrasekhar, S., Ferrari, V. (1984) On the Nutku-Halil solution for colliding impulsive gravitational waves, Proc. Roy. Soc. Lond. A396, 55MathSciNetGoogle Scholar
  242. 242.
    Chandrasekhar, S., Xanthopoulos, B. C. (1986) A new type of singularity created by colliding gravitational waves, Proc. Roy. Soc. Lond. A408, 175MathSciNetGoogle Scholar
  243. 243.
    Chandrasekhar, S., Xanthopoulos, B. C. (1985) On colliding waves in the Einstein-Maxwell theory, Proc. Roy. Soc. Lond. A398, 223MathSciNetGoogle Scholar
  244. 244.
    Bičák, J. (1989) Exact radiative space-times, in Proceedings of the fifth Marcel Grossmann Meeting on General Relativity, eds. D. Blair and M. J. Buckingham, World Scientific, SingaporeGoogle Scholar
  245. 245.
    Yurtsever, U. (1987) Instability of Killing-Cauchy horizons in plane-symmetric spacetimes, Phys. Rev. D36, 1662ADSMathSciNetGoogle Scholar
  246. 246.
    Yurtsever, U. (1988) Singularities in the collisions of almost-plane gravitational waves, Phys. Rev. D38, 1731ADSMathSciNetGoogle Scholar
  247. 247.
    Chandrasekhar, S. (1986) Cylindrical waves in general relativity, Proc. Roy. Soc. Lond. A408, 209MathSciNetGoogle Scholar
  248. 248.
    Einstein, A., Rosen, N. (1937) On Gravitational Waves, J. Franklin Inst. 223, 43MATHCrossRefADSGoogle Scholar
  249. 249.
    Beck, G. (1925) Zur Theorie binärer Gravitationsfelder, Z. Phys. 33, 713CrossRefADSGoogle Scholar
  250. 250.
    Stachel, J. (1966) Cylindrical Gravitational News, J. Math. Phys. 7, 1321MATHCrossRefADSMathSciNetGoogle Scholar
  251. 251.
    d’Inverno, R. (1997) Combining Cauchy and characteristic codes in numerical relativity, in Relativistic Gravitation and Gravitational Radiation (Proceedings of the Les Houches School of Physics), eds. J.-A. Marck and J.-P. Lasota, Cambridge University Press, CambridgeGoogle Scholar
  252. 252.
    Piran, T., Safier, P. N. and Katz, J. (1986) Cylindrical gravitational waves with two degrees of freedom: An exact solution, Phys. Rev. D34, 331ADSGoogle Scholar
  253. 253.
    Thorne, K. S. (1965) C-energy, Phys. Rev. B138, 251ADSCrossRefMathSciNetGoogle Scholar
  254. 254.
    Garriga, J., Verdaguer, E. (1987) Cosmic strings and Einstein-Rosen waves, Phys. Rev. D36, 2250ADSGoogle Scholar
  255. 255.
    Xanthopoulos, B. C. (1987) Cosmic strings coupled with gravitational and electromagnetic waves, Phys. Rev. D35, 3713ADSMathSciNetGoogle Scholar
  256. 256.
    Chandrasekhar, S., Ferrari, V. (1987) On the dispersion of cylindrical impulsive gravitational waves, Proc. Roy. Soc. Lond. A412, 75MathSciNetGoogle Scholar
  257. 257.
    Tod, K. P. (1990) Penrose’s quasi-local mass and cylindrically symmetric spacetimes, Class. Quantum Grav. 7, 2237MATHADSCrossRefMathSciNetGoogle Scholar
  258. 258.
    Berger, B. K., Chruściel, P. T. and Moncrief, V. (1995) On “Asymptotically Flat” Space-Times with G 2-Invariant Cauchy Surfaces, Ann. Phys. (N.Y.) 237, 322MATHADSCrossRefGoogle Scholar
  259. 259.
    Kuchař, K. V. (1971) Canonical quantization of cylindrical gravitational waves, Phys. Rev. D4, 955ADSGoogle Scholar
  260. 260.
    Ashtekar, A., Pierri, M. (1996) Probing quantum gravity through exactly soluble midisuperspaces 1, J. Math. Phys. 37, 6250MATHADSCrossRefMathSciNetGoogle Scholar
  261. 261.
    Korotkin, D., Samtleben, H. (1998) Canonical Quantization of Cylindrical Gravitational Waves with Two Polarizations, Phys. Rev. Lett. 80, 14MATHADSCrossRefMathSciNetGoogle Scholar
  262. 262.
    Ashtekar, A., Bičák, J. and Schmidt, B. G. (1997) Asymptotic structure of symmetry-reduced general relativity, Phys. Rev. D55, 669ADSGoogle Scholar
  263. 263.
    Ashtekar, A., Bičák, J. and Schmidt, B. G. (1997) Behaviour of Einstein-Rosen waves at null infinity, Phys. Rev. D55, 687ADSGoogle Scholar
  264. 264.
    Penrose, R. (1963) Asymptotic properties of fields and space-times, Phys. Rev. Lett. 10, 66; (1965) Zero rest-mass fields including gravitation: asymptotic behaviour, Proc. Roy. Soc. Lond. A284, 159ADSCrossRefMathSciNetGoogle Scholar
  265. 265.
    Ehlers, J., Friedrich, H. eds. (1994) in Canonical Gravity: From Classical to Quantum, Springer-Verlag, Berlin-HeidelbergMATHGoogle Scholar
  266. 266.
    Ryan, M. (1972) Hamiltonian Cosmology, Springer-Verlag, BerlinGoogle Scholar
  267. 267.
    MacCallum, M. A. H. (1975) Quantum Cosmological Models, in Quantum Gravity, eds. C. J. Isham, R. Penrose and D. W. Sciama, Clarendon Press, OxfordGoogle Scholar
  268. 268.
    Halliwell, J. J. (1991) Introductory Lectures on Quantum Cosmology, in Quantum Cosmology and Baby Universes, eds. S. Coleman, J. Hartle, T. Piran and S. Weinberg, World Scientific, SingaporeGoogle Scholar
  269. 269.
    Halliwell, J. J. (1990) A Bibliography of Papers on Quantum Cosmology, Int. J. Mod. Phys. A5, 2473ADSMathSciNetGoogle Scholar
  270. 270.
    Kuchař, K. V. (1973) Canonical Quantization of Gravity, in Relativity, Astrophysics and Cosmology, ed. W. Israel, Reidel, DordrechtGoogle Scholar
  271. 271.
    Kuchař, K. V. (1992) Time and Interpretations of Quantum Gravity, in Proceedings of the 4th Canadian Conference on General Relativity and Relativistic Astrophysics, eds. G. Kunstatter, D. Vincent and J. Williams, World Scientific, SingaporeGoogle Scholar
  272. 272.
    Kuchař, K. V. (1994) Geometrodynamics of Schwarzschild black holes, Phys. Rev. D50, 3961ADSGoogle Scholar
  273. 273.
    Romano, J. D., Torre, C. G. (1996) Internal Time Formalism for Spacetimes with Two Killing Vectors, Phys. Rev. D53, 5634. See also Torre, C. G. (1998) Midi-superspace Models of Canonical Quantum Gravity, gr-qc/9806122ADSMathSciNetGoogle Scholar
  274. 274.
    Louko, J., Whiting, B. F. and Friedman, J. L. (1998) Hamiltonian spacetime dynamics with a spherical null-dust shell, Phys. Rev. D57, 2279ADSMathSciNetGoogle Scholar
  275. 275.
    Griffiths, J. B., Miccicho, S. (1997) The Weber-Wheeler-Bonnor pulse and phase shifts in gravitational soliton interactions, Phys. Lett. A233, 37ADSGoogle Scholar
  276. 276.
    Piran, T., Safier, P. N. and Stark, R. F. (1985) General numerical solution of cylindrical gravitational waves, Phys. Rev. D32, 3101ADSGoogle Scholar
  277. 277.
    Wilson, J. P. (1997) Distributional curvature of time dependent cosmic strings, Class. Quantum Grav. 14, 3337MATHADSCrossRefGoogle Scholar
  278. 278.
    Bičák, J., Schmidt, B. G. (1989) On the asymptotic structure of axisymmetric radiative spacetimes, Class. Quantum Grav. 6, 1547ADSCrossRefMATHGoogle Scholar
  279. 279.
    Bičák, J., Pravdová, A. (1998) Symmetries of asymptotically flat electrovacuum spacetimes and radiation, J. Math. Phys. 39, 6011ADSCrossRefMATHMathSciNetGoogle Scholar
  280. 280.
    Bičák, J., Pravdová, A. (1999) Axisymmetric electrovacuum spacetimes with a translational Killing vector at null infinity, Class. Quantum Grav. 16, 2023ADSCrossRefMATHGoogle Scholar
  281. 281.
    Robinson, I., Trautman, A. (1962) Some spherical gravitational waves in general relativity, Proc. Roy. Soc. Lond. A265, 463; see also [61]MathSciNetGoogle Scholar
  282. 282.
    Chruściel, P. T. (1992) On the global structure of Robinson-Trautman spacetimes, Proc. Roy. Soc. Lond. A 436, 299; Chruściel, P. T., Singleton, D. B. (1992) Non-Smoothness of Event Horizons of Robinson-Trautman Black Holes, Commun. Math. Phys. 147, 137, and references thereinGoogle Scholar
  283. 283.
    Bičák, J., Podolský, J. (1995) Cosmic no-hair conjecture and black-hole formation: An exact model with gravitational radiation, Phys. Rev. D52, 887ADSGoogle Scholar
  284. 284.
    Bičák, J., Schmidt, B. G. (1984) Isometries compatible with gravitational radiation, J. Math. Phys. 25, 600ADSCrossRefMathSciNetGoogle Scholar
  285. 285.
    Bonnor, W. B., Swaminarayan, N. S. (1964) An exact solution for uniformly accelerated particles in general relativity, Zeit. f. Phys. 177, 240. See also the original paper on negative mass in general relativity by Bondi, H. (1957) Rev. Mod. Phys. 29, 423MATHCrossRefADSMathSciNetGoogle Scholar
  286. 286.
    Israel, W., Khan, K. A. (1964) Collinear particles and Bondi dipoles in general relativity, Nuov. Cim. 33, 331MATHCrossRefMathSciNetGoogle Scholar
  287. 287.
    Bičák J. (1985) On exact radiative solutions representing finite sources, in Galaxies, axisymmetric systems and relativity (Essays presented to W. B. Bonnor on his 65th birthday), ed. M. A. H. MacCallum, Cambridge University Press, CambridgeGoogle Scholar
  288. 288.
    Bičák, J., Schmidt, B. G. (1989) Asymptotically flat radiative space-times with boost-rotation symmetry: the general structure, Phys. Rev. D40, 1827ADSGoogle Scholar
  289. 289.
    Bičák J. (1987) Radiative properties of spacetimes with the axial and boost symmetries, in Gravitation and Geometry (A volume in honour of Ivor Robinson), eds. W. Rindler and A. Trautman, Bibliopolis, NaplesGoogle Scholar
  290. 290.
    Bičák, J., Hoenselaers, C. and Schmidt, B. G. (1983) The solutions of the Einstein equations for uniformly accelerated particles without nodal singularities II. Self-accelerating particles, Proc. Roy. Soc. Lond. A390, 411Google Scholar
  291. 291.
    Bičák, J., Reilly, P. and Winicour, J. (1988) Boost rotation symmetric gravitational null cone data, Gen. Rel. Grav. 20, 171CrossRefADSGoogle Scholar
  292. 292.
    Gómez R., Papadopoulos P. and Winicour J. (1994) J. Math. Phys. 35, 4184MATHADSCrossRefMathSciNetGoogle Scholar
  293. 293.
    Alcubierre, M., Gundlach, C. and Siebel, F. (1997) Integration of geodesics as a test bed for comparing exact and numerically generated spcetimes, in Abstracts of Plenary Lectures and Contributed Papers (GR15), Inter-University Centre for Astronomy and Astrophysics Press, PuneGoogle Scholar
  294. 294.
    Bičák, J., Hoenselaers, C. and Schmidt B.G., (1983) The solutions of the Einstein equations for uniformly accelerated particles without nodal singularities I. Freely falling particles in external fields, Proc. Roy. Soc. Lond. A390, 397Google Scholar
  295. 295.
    Bičák, J. (1980) The motion of a charged black hole in an electromagnetic field, Proc. Roy. Soc. Lond. A371, 429Google Scholar
  296. 296.
    Hawking, S. W., Horowitz, G. T. and Ross, S. F. (1995) Entropy, area, and black hole pairs, Phys. Rev. D51, 4302; Mann, R. B., Ross, S. F. (1995) Cosmological production of charged black hole pairs, Phys. Rev. D52, 2254; Hawking, S. W., Ross, S. F. (1995) Pair production of black holes on cosmic strings, Phys. Rev. Lett. 75, 3382ADSMathSciNetGoogle Scholar
  297. 297.
    Plebański, J., Demiański, M. (1976) Rotating, charged and uniformly accelerating mass in general relativity, Ann. Phys. (N.Y.) 98, 98ADSCrossRefMATHGoogle Scholar
  298. 298.
    Bičák, J., Pravda, V. (1999) Spinning C-metric: radiative spacetime with accelerating, rotating black holes, Phys. Rev. D60, 044004Google Scholar
  299. 299.
    Belinsky, V. A., Khalatnikov, I. M. and Lifshitz, E. M. (1970) Oscillatory approach to a singular point in the relativistic cosmology, Adv. in Phys. 19, 525ADSCrossRefGoogle Scholar
  300. 300.
    Belinsky, V. A., Khalatnikov, I. M. and Lifshitz, E. M. (1982) A general solution of the Einstein equations with a time singularity, Adv. in Phys. 31, 639ADSCrossRefGoogle Scholar
  301. 301.
    Ellis, G. F. R. (1996) Contributions of K. Gödel to Relativity and Cosmology, in Gödel’96: Logical Foundations of Mathematics, Computer Science and Physics—Kurt Gödel’s Legacy, ed. P. Hájek, Springer-Verlag, Berlin-Heidelberg; see also preprint 1996/7 of the Dept. of Math. and Appl. Math., University of Cape TownGoogle Scholar
  302. 302.
    Kantowski, R., Sachs, R. K. (1966) Some Spatially Homogenous Anisotropic Relativistic Cosmological Models, J. Math. Phys. 7, 443CrossRefADSMathSciNetGoogle Scholar
  303. 303.
    Thorne, K. S. (1967) Primordial element formation, primordial magnetic fields, and the isotropy of the universe, Astrophys. J. 148, 51ADSCrossRefGoogle Scholar
  304. 304.
    Ryan, M. P., Shepley, L. C. (1975) Homogeneous Relativistic Cosmologies, Princeton University Press, PrincetonGoogle Scholar
  305. 305.
    MacCallum, M. A. H. (1979) Anisotropic and inhomogeneous relativistic cosmologies, in General Relativity (An Einstein Centenary Survey), eds. S. W. Hawking and W. Israel, Cambridge University Press, CambridgeGoogle Scholar
  306. 306.
    Obregón, O., Ryan, M. P. (1998) Quantum Planck size black hole states without a horizon, Modern Phys. Lett. A 13, 3251; see also references thereinADSCrossRefGoogle Scholar
  307. 307.
    Nojiri, S., Obregón, O., Odintsov, S. D. and Osetrin, K. E. (1999) (Non)singular Kantowski-Sachs universe from quantum spherically reduced matter, Phys. Rev. D60, 024008Google Scholar
  308. 308.
    Heckmann, O., Schücking, E. (1962) Relativistic Cosmology, in Gravitation: an introduction to current research, ed. L. Witten, J. Wiley and Sons, New YorkGoogle Scholar
  309. 309.
    Zel’dovich, Ya. B., Novikov, I. D. (1983) Relativistic Astrophysics, Volume 2: The Structure and Evolution of the Universe, The University of Chicago Press, ChicagoGoogle Scholar
  310. 310.
    MacCallum, M. A. H. (1994) Relativistic cosmologies, in Deterministic Chaos in General Relativity, eds. D. Hobill, A. Burd and A. Coley, Plenum Press, New YorkGoogle Scholar
  311. 311.
    Wainwright, J., Ellis, G. F. R. eds. (1997) Dynamical Systems in Cosmology, Cambridge University Press, CambridgeGoogle Scholar
  312. 312.
    Misner, C. W. (1969) Mixmaster universe, Phys. Rev. Lett. 22, 1071MATHADSCrossRefGoogle Scholar
  313. 313.
    Hu, B. L., Ryan, M. P. and Vishveshwara, C. V. eds. (1993) Directions in General Relativity, Vol. 1 (Papers in honor of Charles Misner), Cambridge University Press, CambridgeGoogle Scholar
  314. 314.
    Uggla, C., Jantzen, R. T. and Rosquist, K. (1995) Exact hypersurfacehomogeneous solutions in cosmology and astrophysics, Phys. Rev. D51, 5522ADSMathSciNetGoogle Scholar
  315. 315.
    Tanaka, T., Sasaki, M. (1997) Quantized gravitational waves in the Milne universe, Phys. Rev. D55, 6061ADSGoogle Scholar
  316. 316.
    Lukash, V. N. (1975) Gravitational waves that conserve the homogeneity of space, Sov. Phys. JETP 40, 792ADSMathSciNetGoogle Scholar
  317. 317.
    Barrow, J. D., Sonoda, D. H. (1986) Asymptotic stability of Bianchi type universes, Physics Reports 139, 1ADSCrossRefMathSciNetGoogle Scholar
  318. 318.
    Kuchař, K. V., Ryan, M. P. (1989) Is minisuperspace quantization valid?: Taub in Mixmaster, Phys. Rev. D40, 3982. The approach was first used in Kuchař, K. V., Ryan, M. P. (1986) Can Minisuperspace Quantization be Justified?, in Gravitational Collapse and Relativity, eds. H. Sato and T. Nakamura, World Scientific, SingaporeADSGoogle Scholar
  319. 319.
    Bogoyavlenski, O. I. (1985) Methods in the Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics, Springer-Verlag, BerlinGoogle Scholar
  320. 320.
    Hobill, D., Burd, A. and Coley, A. eds. (1994) Deterministic Chaos in General Relativity, Plenum Press, New YorkGoogle Scholar
  321. 321.
    Rendall, A. (1997) Global dynamics of the Mixmaster model, Class. Quantum Grav. 14, 2341MATHADSCrossRefMathSciNetGoogle Scholar
  322. 322.
    Khalatnikov, I. M., Lifshitz, E. M., Khamin, K. M., Shehur, L. N. and Sinai, Ya. G. (1985) On the Stochasticity in Relativistic Cosmology, J. of Statistical Phys. 38, 97CrossRefADSGoogle Scholar
  323. 323.
    LeBlanc, V. G., Kerr, D. and Wainwright, J. (1995) Asymptotic states of magnetic Bianchi VI0 cosmologies, Class. Quantum Grav. 12, 513MATHADSCrossRefMathSciNetGoogle Scholar
  324. 324.
    LeBlanc, V. G. (1977) Asymptotic states of magnetic Bianchi I cosmologies, Class. Quantum Grav. 14, 2281ADSCrossRefMathSciNetGoogle Scholar
  325. 325.
    Jantzen, R. T. (1986) Finite-dimensional Einstein-Maxwell-scalar field system, Phys. Rev. D33, 2121ADSMathSciNetGoogle Scholar
  326. 326.
    LeBlanc, V. G. (1998) Bianchi II magnetic cosmologies, Class. Quantum Grav. 15, 1607MATHADSCrossRefMathSciNetGoogle Scholar
  327. 327.
    Belinsky, V. A., Khalatnikov, I. M. (1973) Effect of scalar and vector fields on the nature of the cosmological singularity, Soviet Physics JETP 36, 591ADSMathSciNetGoogle Scholar
  328. 328.
    Berger, B. K. (1999) Influence of scalar fields on the approach to a cosmological singularity, gr-qc/9907083Google Scholar
  329. 329.
    Wainwright, J., Coley, A. A., Ellis, G. F. R. and Hancock, M. (1998) On the isotropy of the Universe: do Bianchi VIIh cosmologies isotropize? Class. Quantum Grav. 15, 331MATHADSCrossRefMathSciNetGoogle Scholar
  330. 330.
    Weaver, M., Isenberg, J. and Berger, B. K. (1998) Mixmaster Behavior in Inomogeneous Cosmological Spacetimes, Phys. Rev. Lett. 80, 2984ADSCrossRefGoogle Scholar
  331. 331.
    Berger, B. K., Moncrief, V. (1998) Evidence for an oscillatory singularity in generic U(1) cosmologies on T 3 × R, Phys. Rev. D58, 064023Google Scholar
  332. 332.
    Gowdy, R. H. (1971) Gravitational Waves in Closed Universes, Phys. Rev. Lett. 27, 826; Gowdy, R. H. (1974) Vacuum Spacetimes with Two-Parameter Spacelike Isometry Groups and Compact Invariant Hypersurfaces: Topologies and Boundary Conditions, Ann. Phys. (N.Y.) 83, 203ADSCrossRefGoogle Scholar
  333. 333.
    Carmeli, M., Charach, Ch. and Malin, S. (1981) Survey of cosmological models with gravitational scalar and electromagnetic waves, Physics Reports 76, 79ADSCrossRefMathSciNetGoogle Scholar
  334. 334.
    Chruściel, P. T. (1990) On Space-Times with U(1)×U(1) Symmetric Compact Cauchy Surfaces, Ann. Phys. (N. Y.) 202, 100ADSCrossRefMATHGoogle Scholar
  335. 335.
    Gowdy, R. H. (1975) Closed gravitational-wave universes: Analytic solutions with two-parameter symmetry, J. Math. Phys. 16, 224ADSCrossRefGoogle Scholar
  336. 336.
    Charach,&Ch. (1979) Electromagnetic Gowdy universe, Phys. Rev. D19, 3516ADSGoogle Scholar
  337. 337.
    Bičák, J., Griffiths, J. B. (1996) Gravitational Waves Propagating into Friedmann-Robertson-Walker Universes, Ann. Phys. (N.Y) 252, 180ADSCrossRefMATHGoogle Scholar
  338. 338.
    Berger, B. K., Chruściel, P. T., Isenberg, J. and Moncrief, V. (1997) Global Foliations of Vacuum Spacetimes with T 2 Isometry, Ann. Phys. (N.Y.) 260, 117MATHADSCrossRefGoogle Scholar
  339. 339.
    Chruściel, P. T., Isenberg, J. and Moncrief, V. (1990) Strong cosmic censorship in polarized Gowdy spacetimes, Class. Quantum Grav. 7, 1671ADSCrossRefMATHGoogle Scholar
  340. 340.
    Moncrief, V. (1997) Spacetime Singularities and Cosmic Censorship, in Proc. of the 14th International Conference on General Relativity and Grativation, eds. M. Francaviglia, G. Longhi, L. Lusanna and E. Sorace, World Scientific, SingaporeGoogle Scholar
  341. 341.
    Kichenassamy, S., Rendall, A. D. (1998) Analytic description of singularities in Gowdy spacetimes, Class. Quantum Grav. 15, 1339MATHADSCrossRefMathSciNetGoogle Scholar
  342. 342.
    Kichenassamy, S. (1996) Nonlinear Wave Equations, Marcel Dekker Publ. New YorkMATHGoogle Scholar
  343. 343.
    Adams, P. J., Hellings, R. W., Zimmermann, R. L., Farhoosh, H., Levine, D. I. and Zeldich, S. (1982) Inhomogeneous cosmology: gravitational radiation in Bianchi backgrounds, Astrophys. J. 253, 1ADSCrossRefGoogle Scholar
  344. 344.
    Belinsky, V., Zakharov, V. (1978) Integration of the Einstein equations by means of the inverse scattering problem technique and construction of exact soliton solutions, Sov. Phys. JETP 48, 985ADSGoogle Scholar
  345. 345.
    Carr, B. J., Verdaguer, E. (1983) Soliton solutions and cosmological gravitational waves, Phys. Rev. D28, 2995ADSMathSciNetGoogle Scholar
  346. 346.
    Belinsky, V. (1991) Gravitational breather and topological properties of gravisolitons, Phys. Rev. D44, 3109ADSMathSciNetGoogle Scholar
  347. 347.
    Kordas, P. (1993) Properties of the gravibreather, Phys. Rev. D48, 5013ADSGoogle Scholar
  348. 348.
    Alekseev, G. A. (1988) Exact solutions in the general theory of relativity, Proceedings of the Steklov Institute of Mathematics, Issue 3, p. 215Google Scholar
  349. 349.
    Verdaguer, E. (1993) Soliton solutions in spacetimes with spacelike Killing fields, Physics Reports 229, 1ADSCrossRefMathSciNetGoogle Scholar
  350. 350.
    Katz, J., Bičák, J. and Lynden-Bell, D. (1997) Relativistic conservation laws and integral constraints for large cosmological perturbations, Phys. Rev. D55, 5957ADSGoogle Scholar
  351. 351.
    Uzan, J. P., Deruelle, M. and Turok, N. (1998) Conservation laws and cosmological perturbations in curved universes, Phys. Rev. D57, 7192ADSMathSciNetGoogle Scholar
  352. 352.
    Beig, R., Simon, W. (1992) On the Uniqueness of Static Perfect-Fluid Solutions in General Relativity, Commun. Math. Phys. 144, 373MATHADSCrossRefMathSciNetGoogle Scholar
  353. 353.
    Lindblom, L., Masood-ul-Alam (1994) On the Spherical Symmetry of Static Stellar Models, Commun. Math. Phys. 162, 123MATHADSCrossRefMathSciNetGoogle Scholar
  354. 354.
    Rendall A. (1997) Solutions of the Einstein equations with matter, in Proc. of the 14th International Conference on General Relativity and Gravitation, eds. M. Francaviglia, G. Longhi, L. Lusanna and E. Sorace, World Scientific, SingaporeGoogle Scholar
  355. 355.
    Bartnik, R., McKinnon, J. (1988) Particlelike Solutions of the Einstein-Yang-Mills Equations, Phys. Rev. Lett. 61, 141ADSCrossRefMathSciNetGoogle Scholar
  356. 356.
    Volkov, M. S., Gal’tsov, D. V. (1999) Gravitating Non-Abelian Solitons and Black Holes with Yang-Mills Fields, Physics Reports 319, 1ADSCrossRefMathSciNetGoogle Scholar
  357. 357.
    Rendall, A. D., Tod, K. P. (1999) Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric, Class. Quantum Grav. 16, 1705MATHADSCrossRefMathSciNetGoogle Scholar
  358. 358.
    Carr, B. J., Coley, A. A. (1999) Self-similarity in general relativity, Class. Quantum Grav. 16, R 31ADSCrossRefMathSciNetGoogle Scholar
  359. 359.
    Gundlach, C. (1998) Critical Phenomena in Gravitational Collapse, Adv. Theor. Math. Phys. 2, 1MATHMathSciNetGoogle Scholar
  360. 360.
    Krasiński, A. (1997) Inhomogeneous Cosmological Models, Cambridge University Press, CambridgeMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Jiří Bičák
    • 1
  1. 1.Institute of Theoretical PhysicsCharles UniversityPrague

Personalised recommendations